You can check that you have a correct answer by taking the derivative.
Notice that if you take the derivative of or both derivatives are zero. Also notice that if you were given limits of integration you would end up with
In my opinion I always combine constants in my
Possibly the OP simplified
which should have been
[Edit: no, that doesn't explain it.]
Anyway, just in case a picture helps...
... where (key in spoiler) ...
Further edit: (See below.) Yes, false alarm. Substituting where they did, the OP integrated kind of like this:
... so the sixth was just an extra constant as The Empty Set at first thought. Pardon the fuss.
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!